For \(h_n=0\) , this problem is a weighted \(\mathtt {MaxCut}\)  with given sizes of partitions [1]} (\(\mathtt {WeightedMaxCutGSP}\) ). It can also be seen as a Markowitzian portfolio optimization problem [2]} where the task is to select the best performing \(\kappa \)  of assets in a pool assuming correlations between their performance indicators. Note that while for small \(\kappa \)  the problem is clearly tractable, for the case \(\kappa =N/2\)  the problem turns into the NP-Hard \(\mathtt {GraphBisection}\) , which has been mapped to QAOA and studied numerically in the unweighted case where \(J_{nm}\)  are either 0 or 1 using a sparse XY-mixer in [3]}.
